The sauces are called chutney (plural chutneys).
The green one, called hari chutney in Hindi, is generally made with a mixture of coriander (cilantro) leaves and mint leaves. Hari means green in Hindi. The leaves (I have used them in a 3:1::coriander:mint ratio) are ground to a fine paste along with a tbsp of sugar, a pinch of salt, and about 2 tbsp of lime juice (to prevent oxidation of the ground greens and to provide a tangy taste). Some variations of this may add ginger (for flavor) or peanuts (as a thickening agent) to the mixture.
The red chutney, called imli chutney in Hindi, is very often made with the juice of tamarind (imli in Hindi). Tamarind is soaked in water, strained and mixed with sugar, rock salt, toasted and ground cumin, dry powdered ginger, and powdered pepper. Rock salt and dry ginger give this chutney its distinct taste. Very often restaurants add artificial red color to this chutney to turn the color from brown to red.